Page 46 - Anatomy of a Robot

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Moving mass (kinetic energy)
The energy in a moving mass is
E 0.5 m v 2 CONTROL SYSTEMS 31
where m is the mass, which will be described later in the book. v is the velocity.
Note that a moving mass might not just be moving linearly. It might also be
rotating. As such, you can model the energy of both motions separately. You can
use the center of gravity of the mass and see how fast that is moving linearly.
Then you can add the energy of rotation about that center of mass (as you find
it).
Mass at heights (potential energy) When a mass is at a height, the potential
energy it has is given by the equation

E m g h
2
where M is its mass. g is the acceleration constant of gravity (32 ft/sec ). h is
the height the mass might fall. A nice treatment of potential and kinetic energy
can be found at www.dcate.net/coasters/pe.html.
Force evaluation Instead of looking at energy, we’re going to use the technique
of looking at everything in terms of force. We need only to characterize the forces
within the system as they act together. In this way, we can predict what the pieces
of the robot will do. Here are some of the places force is stored in a robot:
Motor force Most motors will generate a time-varying force when energy is
applied. The force might be rotational or linear. To keep matters simple, we’ll
be looking at linear force, such as might be applied by a solenoid, which is an
electromagnet with a moving metal core, much like Figure 2-23.
Moving mass force (kinetic force) Newton created the equation for force
acting on a mass (or mass creating a force):
F m A

where m is the mass and A is the acceleration (or deceleration). When gravity
is the force providing the acceleration, A g and thus F m g, the force
needed to hold up a mass m.
Spring force A spring with a spring constant of K will have a force

F K x
where x is the compression (or elongation) of the spring.
Friction force Friction is a force that is engendered by velocity through a
friction medium. For example, a motor, when the power is turned off, will cause
the vehicle to coast to a stop because its rotor glides over the bearings and the